algorithm - Time Complexity of Dependent for loop -

string str = "abcdefghijklmnopqrstuvwxyz"; int sum = 0; for(int i=0; i<str.length; i++) {     int val = str[i];     while(val > 0)     {        sum = val % 62;        val = val / 62;     } } 

i know parent loop executes n+1 time , child loop executes (val)^(1/62) times. parent loop time complexity o(n) don't find way calculate child loop. so, time complexity of above program ?.

thanks in advance.

let length of string written n.

n = str.length(); 

now, outer for-loop iterates whole length of string,i.e., n times. hence,outer for-loop complexity o(n).

talking child loop, inner while loop executes (val)^(1/62) times. so, can consider inner while-loop complexity o(log₆₂ val).

all other statements take constant time-complexity.

therefore,net time complexity = o(n * log₆₂ val).

last step because of :-

if f1(n) = o(g1(n)) , f2(n) = o(g2(n)),then f1(n) * f2(n) = o(g1(n) * g2(n))

as mentioned edward doolittle in comment, reduce o(n * log₂ val) log bases can converted base 2 constant division(by log₂62).